It is 99 down, 10 to go for Roger Federer, which is, of course, only one way of looking at things at this late stage in the Federer game.

He has chased only a few tennis records with genuine intent, including the men’s mark for Grand Slam singles titles, which Pete Sampras once held with 14 and which Federer now owns with 20.

But Jimmy Connors’s Open-era men’s record of 109 titles has hardly been Federer’s white whale, some career-long obsession that has kept him up nights or inspired him to do a round of extra sprints in Dubai, United Arab Emirates, with the fitness coach Pierre Paganini.

“Either it happens or it doesn’t,” he told Germany’s Tennis Magazin this year, referring to the 109. “If that was really my ultimate goal, I would play a lot more smaller tournaments and in extreme cases, skip all the Masters 1000s and play just 250s and 500s.”

Early in his career, Federer already was sounding blasé about tennis math.

“There are a lot of numbers,” Federer said in an interview after winning the United States Open in 2005 when presented with some of his already-flashy statistics.

But that does not mean Connors’s 109 is not a worthy target.

“It just shows you how good Connors was for so long and how much of a great competitor he was,” said Darren Cahill, the ESPN analyst who coached the former men’s No. 1 Andre Agassi and now coaches the women’s No. 1, Simona Halep. “The fact Connors managed to win 109 in that tough era with McEnroe, Borg and Lendl and the competition he had is remarkable. He might have played a lot more smaller tournaments in those days, where a lot of the Europeans didn’t come across to play in the U.S. But I think Connors’s record will stand up against any of the great records in tennis to be honest.”

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Jimmy Connors won the men’s singles title at Wimbledon in 1982.CreditActionPlus/Corbis, via Getty Images

For now, with the ATP Finals about to begin in London on Sunday, Connors’s record is visible on the horizon, but hardly close enough to touch for Federer. Ten more titles is a big task at age 37 with a limited tournament schedule, and there are plenty of other obstacles beyond his direct control.

Novak Djokovic is back at No. 1 and continues to have the upper hand as he showed by beating Federer for the fourth straight time by winning a taut, three-set semifinal at the Paris Masters on Saturday. Although the new generation of players has yet to win a major singles title, the youngsters are making inroads elsewhere with Alexander Zverev, 21, and Karen Khachanov, 22, winning Masters 1000 titles in 2018 and with Borna Coric, 21, beating Federer twice.

It will only get harder for Federer to reach the finish lines, but he, like Connors, is an exceptional talent with exceptional footwork and staying power, and, for the moment, they have a strikingly similar gap between their first and last tour titles.

Connors won his first in 1972 in Jacksonville, Fla., at age 19 and his last in 1989 at 37 in Tel Aviv. Federer won his first in Milan in 2001 at age 19 and his most recent in Basel at 37 at last month’s Swiss Indoors.

“For me, if they’re chasing me and my accomplishments then what else could I ask for?” Connors said recently. “Would I like 109 to live forever? Sure, why wouldn’t I? I’d be crazy not to.”

At this stage, Federer would be delighted simply to get to 100, which would make him the second man in the 50-year Open era to reach triple figures in singles titles.

Three women have done it: Steffi Graf with 107, Chris Evert with 157 and Martina Navratilova with 167. Evert’s and Navratilova’s gargantuan totals are a reflection of just how long they dominated and how many tournaments they played each year in support of their tour.

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Roger Federer departed the U.S. Open in New York last September. He lost the men’s singles match there to John Millman of Australia.CreditEduardo Munoz Alvarez/Agence France-Presse — Getty Images

Federer is picking his spots, and if he is going to keep heavily prioritizing the most prestigious events — the Grand Slam tournaments and Masters 1000s — and add only his hometown tournament in Basel and a smattering of lower-level grass-court tournaments on the side, then the odds of reaching 109 lengthen.

Federer won seven titles in his dreamy 2017 comeback season. He has won four this year, including the Australian Open, in what has been a less consistently transcendent campaign.

To match Connors, Federer would need two more similarly productive seasons if he were to play through 2020: a reasonable assumption with the Olympics in Tokyo that year and the Olympic gold medal in singles the only major tennis prize Federer lacks (he also has a new megadeal with a Japanese sponsor: Uniqlo).

“To start with it’s insane what Fed is still doing at 37,” said Brad Gilbert, an ESPN analyst and longtime coach. “To win nine or 10 titles in two years is going to be difficult, but I wouldn’t put it past him if he navigates the schedule and plays a few smaller events. If he stays healthy and plays three more years through 2021 and plays until age 40, then I honestly think he does it. What really helps him is that he’s able to take these long breaks and still play at such a high level. Over all, I would think it’s 50-50.”

It has taken Federer longer to hit cruising speed in the second half of 2018, perhaps in part because of a hand injury that he said had affected his forehand during the summer.

He went out in a puddle of sweat in the fourth round of the U.S. Open, losing to the unseeded John Millman. Federer made errors in bunches in his semifinal loss to Coric in Shanghai and looked shaky again early in the week in Basel. His most encouraging recent performance was in defeat against Djokovic in Paris, where he saved all 12 break points he faced before losing his way in the decisive third-set tiebreaker.

Federer was quick off the mark throughout that duel, unquestionably one of the matches of the year. He was deft at the net and able to consistently produce clean backhand drives despite maintaining his position very tight to the baseline.

It will take more of the same to win No. 100 against Djokovic and the rest of the elite eight in London, much more of the same to catch Connors with Federer’s biological clock ticking, ticking.

A version of this article appears in print on , on Page D5 of the New York edition with the headline: Federer Has Path to Connors’s 109-Title Record. Order Reprints | Today’s Paper | Subscribe